We also discuss the convergence rate. Note that \(A\)  is dominated by the fourth term, \(\sqrt{n}/K^{2/5}\) , so it is clear that (REF ) and () converge at a rate of \(\mathcal {O}(\sqrt{n}K^{-2/5})\) . We give special attention to (). Apart from the \(\frac{8b_0^2}{(-\mu _{\ell }+\rho )^2}\)  term, we see that the RHS of () converges at a rate of \(\mathcal {O}(\sqrt{n}K^{-2/5})\) . To understand the convergence of this term, we turn to (REF ) from Assumption 3. As discussed in Section E.4 of the Appendix in [1]}, \(b_k\)  can be made arbitrarily small by running more iterations of the subroutine for estimating \(h_x^k\) . Therefore, as long as we run enough iterations such that \(b_k^2 \le \alpha \) , () will also converge at a rate of \(\mathcal {O}(\sqrt{n}K^{-2/5})\) .
